174 



ALTERNATING CURRENTS 



same emf. per turn in each winding. The total induced emf. in 

 each winding must then be proportional to the number of turns 

 in that winding. That is, 



= & (45) 



where E\ and E% are the primary and secondary induced emfs. 

 and NI and JV 2 are the number of turns in primary and secondary 

 respectively. In the ordinary transformer, the terminal voltage 

 differs from the induced emf. only by a very small percentage, so 

 that for most practical purposes it may be said that the primary 

 and secondary terminal voltages are proportional to the respec- 

 tive number of turns. 



The induced electromotive force in a transformer is propor- 

 tional to three factors; the flux, the frequency, and the number 

 of turns. The complete equation for the induced electromotive 

 force, assuming a sine wave, is as follows: 



E = 4A4fN<f> max 10~ 8 volts (46) 



FIG. 171. Sinusoidal variation of flux with time. 



where / is the frequency in cycles per second, N is the number of 

 turns, and <t> max is the maximum value of the flux in the core. 

 The factor 4.44 is 4 times the form factor, which is 1.11 for a sine 

 wave. (See Chap. 1, Par. 5, page 10.) 



This equation is derived as follows: 



Figure 171 shows the mutual flux < varying sinusoidally with 

 the time. Between points a and b the total change of flux is 

 2 <t> max lines or maxwells. This change of flux occurs in half a 



